Mr Kenny made the comments as political parties united in grief after Britain suffered its third terrorist attack in less than three months, and the second in the space of two weeks.
In a statement as he began a two-day US trade mission to Chicago, Mr Kenny said the attack in London would be condemned by any right-minded person.
He insisted those behind the attacks do not represent the Muslim community and are part of a “warped world view”.
“We utterly condemn the cowardly attack in London and reject the warped motives and world view behind them. This is sheer madness.
“Ireland will continue to work exceptionally closely with the UK and all of our colleagues on security matters and prevention as far as possible. I have been in contact with the Tánaiste and Minister for Justice Frances Fitzgerald and will speak to Prime Minister Theresa May when appropriate. The Irish people stand with our close neighbours once again,” he said.
His replacement, incoming taoiseach Leo Varadkar, was equally clear in his condemnation “in the strongest possible terms”, saying the loss of life is “horrific”.
“Once again innocent people have been targeted in the most craven and horrific manner. We extend our solidarity to the people of the UK and condemn this incident in the strongest possible terms.
“The fact that this comes so soon after the Manchester attack only adds to the horror,” he said.
President Michael D Higgins expressed the “heartfelt sympathy and support of the Irish people” to the victims of the attack, saying what happened on Saturday night “will be rightly condemned by all”, a view repeated by Justice Minister Frances Fitzgerald and Foreign Affairs Minister Charlie Flanagan.
Fianna Fáil leader Micheál Martin said the “callous” attack on a city that is home to millions of diverse people must be condemned.
Citing London’s history of withstanding attacks in the past, he said it will “bring Londoners of all creeds, races and ethnicities even more together” in direct opposition to terrorism.
“London is home is millions, many of whom who are Irish or of Irish descent. We know from our own past that the best response to terror is to be open, tolerant and to stand united.
“Those who orchestrated this attack and the previous attack in Manchester are cowards. The people of London have, in the few short hours since last night’s attack, shown the world what true courage and bravery is,” he said.
Similarly, Labour leader Brendan Howlin, Sinn Fein leader Gerry Adams and a number of other opposition TDs were similarly united in their revulsion of what happened, saying innocent people of regardless of their religion, race, ethnicity and upbringing must be protected from extremism in all its forms.
“The attack on people enjoying a Saturday night out was mindlessly cruel. But the response it triggered from emergency services and the people of London showed the futility of this action,” said Mr Howlin.
“London has long stood as a beacon of inclusion and possibility. It will continue to be that, long after this cowardly attack is forgotten,” he said.
Cabinet is expected to re-examine Ireland’s security measures in light of the latest attack in Britain, although no changes are expected.